ENERGY-MOMENTUM TENSOR IN CONFORMAL FIELD-THEORIES NEAR A BOUNDARY

The requirements of conformal invariance for the two-point function of the energy-momentum tensor in the neighbourhood of a Plane boundary are investigated, restricting the conformal group to those transformations leaving the boundary invariant. It is shown that the general solution may contain an arbitrary function of a single conformally invariant variable upsilon, except in dimension 2. The functional dependence on upsilon is determined for free scalar and fermion fields in arbitrary dimension d and also to leading order in the epsilon-expansion about d = 4 for the nongaussian fixed point in phi4 theory. The two-point correlation function of the energy-momentum tensor and a scalar field is also shown to have a unique expression in terms of upsilon and the overall coefficient is determined by the operator product expansion. The energy-momentum tensor on a general curved manifold is further discussed by considering variations of the metric. In the presence of a boundary this procedure naturally defines extra boundary operators. By considering diffeomorphisms these are related to components of the energy-momentum tensor on the boundary. The implications of Weyl invariance in this framework are also derived.